In grammar the term complement is sometimes used with different meanings. The core meaning of complement is for a word, phrase or clause which is necessary in a sentence to complete its meaning. We find complements which function as a sentence element (i.e. of equal status to subjects, verbs and objects) and complements which exist within sentence elements.
Complements which are sentence elements
A subject complement tells more about the subject by means of the verb. In the examples below the sentence elements are (SUBJECT + VERB + COMPLEMENT)
Mr Smith is a management consultant. (a predicative nominal)
She looks ill. (a predicative adjective)
An object complement tells us more about the object by means of the verb. In the examples below the sentence elements are (SUBJECT + VERB + OBJECT + COMPLEMENT). Object complements can often be removed leaving a well-formed sentence, thus the use of the term complement is slightly illogical.
We elected him chairman. (a predicative nominal)
We painted the house white. (a predicative adjective)
Adverbials are usually an adjuncts (i.e. they can be removed and a well-formed sentence remains). In the following sentence both adverbial adjuncts can be removed and a properly formed sentence remains.
Yesterday I saw Anna at the station.
If, however, an adverbial is a necessary sentence element then it is correctly referred to as a complement. The structure of the sentence below is (SUBJECT + VERB + ADVERBIAL COMPLEMENT)
John put the basket in the garden. (i.e. John put the basket is not a properly formed sentence)